Mixture Ratio Estimators Using  Multi-Auxiliary Variables and Attributes for Two-Phase Sampling

Paul Mwangi Waweru; John Kung’u; James Kahiri

doi:10.4236/ojs.2014.49073

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Open Journal of Statistics > Vol.4 No.9, October 2014

Mixture Ratio Estimators Using Multi-Auxiliary Variables and Attributes for Two-Phase Sampling ()

Paul Mwangi Waweru, John Kung’u, James Kahiri

Department of Statistics and Actuarial Science, Kenyatta University, Nairobi, Kenya.

DOI: 10.4236/ojs.2014.49073 PDF HTML XML 3,580 Downloads 4,232 Views Citations

Abstract

In this paper, we have proposed three classes of mixture ratio estimators for estimating population mean by using information on auxiliary variables and attributes simultaneously in two-phase sampling under full, partial and no information cases and analyzed the properties of the estimators. A simulated study was carried out to compare the performance of the proposed estimators with the existing estimators of finite population mean. It has been found that the mixture ratio estimator in full information case using multiple auxiliary variables and attributes is more efficient than mean per unit, ratio estimator using one auxiliary variable and one attribute, ratio estimator using multiple auxiliary variable and multiple auxiliary attributes and mixture ratio estimators in both partial and no information case in two-phase sampling. A mixture ratio estimator in partial information case is more efficient than mixture ratio estimators in no information case.

Keywords

Ratio Estimator, Multiple Auxiliary Variables, Multiple Auxiliary Attributes, Two-Phase Sampling, Bi-Serial Correlation Coefficient

Share and Cite:

Waweru, P. , Kung’u, J. and Kahiri, J. (2014) Mixture Ratio Estimators Using Multi-Auxiliary Variables and Attributes for Two-Phase Sampling. Open Journal of Statistics, 4, 776-788. doi: 10.4236/ojs.2014.49073.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Neyman, J. (1938) Contribution to the Theory of Sampling Human Populations. Journal of the American Statistical Association, 33, 101-116. http://dx.doi.org/10.1080/01621459.1938.10503378
[2]	Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. Journal of Agricultural Science, 30, 262-275. http://dx.doi.org/10.1017/S0021859600048012
[3]	Hansen, M.H. and Hurwitz, W.N. (1943) On the Theory of Sampling from Finite Populations. Annals of Mathematical Statistics, 14, 333-362. http://dx.doi.org/10.1214/aoms/1177731356
[4]	Watson, D.J. (1937) The Estimation of Leaf Areas. Journal of Agricultural Science, 27, 474. http://dx.doi.org/10.1017/S002185960005173X
[5]	Olikin, I. (1958) Multivariate Ratio Estimation for Finite Population. Biometrika, 45, 154-165. http://dx.doi.org/10.1093/biomet/45.1-2.154
[6]	Raj, D. (1965) On a Method of Using Multi-Auxiliary Information in Sample Surveys. Journals of the American Statistical Association, 60, 154-165. http://dx.doi.org/10.1080/01621459.1965.10480789
[7]	Singh, M.P. (1967) Ratio-Cum-Product Method of Estimation. Metrika, 12, 34-42. http://dx.doi.org/10.1007/BF02613481
[8]	Robson, D.S. (1952) Multiple Sampling of Attributes. Journal of the American Statistical Association, 47, 203-215. http://dx.doi.org/10.1080/01621459.1952.10501164
[9]	Ahmad, Z. (2008) Generalized Multivariate Ratio and Regression Estimators for Multi-Phase Sampling. Unpublished Ph.D. Thesis, National College of Business Administration and Economics, Lahore.
[10]	Zahoor, A., Muhhamad, H. and Munir, A. (2009) Generalized Regression-Cum-Ratio Estimators for Two Phase Sampling Using Multiple Auxiliary Variables. Pakistan Journal of Statistics, 25, 93-106.
[11]	Jhajj, H.S., Sharma, M.K. and Grover, L.K. (2006) A Family of Estimator of Population Mean Using Information on Auxiliary Attributes. Pakistan Journal of Statistics, 22, 43-50.
[12]	Naik, V.D. and Gupta, P.C. (1996) A Note on Estimation of Mean with Known Population of Auxiliary Character. Journal of the Indian Society of Agricultural Statistics, 48, 151-158.
[13]	Bahl, S. and Tuteja, R.K. (1991) Ratio and Product Type Estimator. Information and Optimization Sciences, 12, 159-163.
[14]	Hanif, M., Haq, I.U. and Shahbaz, M.Q. (2009) On a New Family of Estimator Using Multiple Auxiliary Attributes. World Applied Science Journal, 11, 1419-1422.
[15]	Kung’u, J. and Odongo, L. (2014) Ratio-Cum-Product Estimator Using Multiple Auxiliary Attributes in Single Phase Sampling. Open Journal of Statistics, 4, 239-245. http://dx.doi.org/10.4236/ojs.2014.44023
[16]	Kung’u, J. and Odongo, L. (2014) Ratio-Cum-Product Estimator Using Multiple Auxiliary Attributes in Two-Phase Sampling. Open Journal of Statistics, 4, 246-257. http://dx.doi.org/10.4236/ojs.2014.44024
[17]	Moeen, M., Shahbaz, Q. and Hanif, M. (2012) Mixture Ratio and Regression Estimators Using Multi-Auxiliary Variable and Attributes in Single Phase Sampling. World Applied Sciences Journal, 18, 1518-1526.
[18]	Simiuddin, M. and Hanif, M. (2007) Estimation of Population Mean in Single and Two Phase Sampling with or without Additional Information. Pakistan Journal of Statistics, 23, 99-118.
[19]	Arora, S. and Lal, B. (1989) New Mathematical Statistics. Satya Prakashan, New Delhi.